Expression of type ExprTuple

from the theory of proveit.linear_algebra.vector_sets

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, V
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import LinDepSets, SpanningSets
from proveit.logic import InSet, NotInSet, Set

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
expr = ExprTuple(InSet(sub_expr1, SpanningSets(V)), NotInSet(sub_expr1, LinDepSets(V)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{SpanningSets}\left(V\right), \left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \notin \textrm{LinDepSets}\left(V\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	8, 7
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operand: 16
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operand: 16
10	Literal
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	16
15	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
16	Variable
17	Lambda	parameter: 23 body: 20
18	Literal
19	Variable
20	IndexedVar	variable: 21 index: 23
21	Variable
22	ExprTuple	23
23	Variable